An object floating in midair underneath an electromagnet is intriguing and mysterious. Students love it, though anyone who has worked with this system soon realizes that the system is only stable over a limited region of space. But why is the system stable in the first place? This paper presents an investigation of the instability of magnetically suspended systems beginning with the simple, and going deeper, leading finally to a computer-controlled solution. The analysis is suitable for use in a college-level introductory physics course in that it relates to the study of damped simple harmonic oscillators. I describe construction of an Arduino-based magnetic levitation apparatus, programs to operate it, and a new procedure for deriving the tuning constants.
The search for a stable magnetic suspension system begins with two ring magnets supported on a vertical pencil, one above the other, with identical poles facing each other. If you support the...